Methods for sourceless density downhole measurement using pulsed neutron generator

A method for estimating a density of an earth formation penetrated by a borehole, the method comprising:

• conveying a carrier through the borehole;
• emitting a pulse of fast neutrons into the formation during a neutron-pulse time interval using a pulsed-neutron source disposed at the carrier;
• detecting gamma-rays due to inelastic scattering and thermal capture of the emitted neutrons in the formation with a gamma-ray detector to provide a gamma-ray energy spectrum due to the inelastic scattering and the thermal capture during a first time interval within the neutron-pulse time interval and to provide a time spectrum of counts or count rates due to thermal capture during a second time interval occurring after the neutron-pulse time interval;
• determining a macroscopic capture cross section ΣF of the formation from a decay in the time spectrum of counts or count rates;
• determining a weight fraction for one or more elements in the formation from the gamma-ray energy spectrum;
• estimating the density of the formation using the macroscopic capture cross section and the weight fraction for the one or more elements;
• decomposing the gamma-ray energy spectrum to a yield of each element contributing to the gamma-ray energy spectrum;
• and
• determining a weight fraction for each elemental yield using calibration data for a configuration of the pulsed-neutron source and the gamma-ray detector used to obtain the gamma-ray energy spectrum.

A method for estimating a density of an earth formation penetrated by a borehole, the method comprising:

• conveying a carrier through the borehole;
• emitting a pulse of fast neutrons into the formation during a neutron-pulse time interval using a pulsed-neutron source disposed at the carrier;
• detecting gamma-rays due to inelastic scattering and thermal capture of the emitted neutrons in the formation with a gamma-ray detector to provide a gamma-ray energy spectrum due to the inelastic scattering and the thermal capture during a first time interval within the neutron-pulse time interval and to provide a time spectrum of counts or count rates due to thermal capture during a second time interval occurring after the neutron-pulse time interval;
• determining a macroscopic capture cross section ΣF of the formation from a decay in the time spectrum of counts or count rates;
• determining a weight fraction for one or more elements in the formation from the gamma-ray energy spectrum and
• estimating the density of the formation using the macroscopic capture cross section and the weight fraction for the one or more elements;
• wherein estimating the density of the formation comprises solving the following equation where f i is the weight fraction of the i-th element, σis the microscopic cross section of the i-th element in barns, Ai is the atomic mass of the i-th element in grams/mole, NA is Avogadro's number, ΣF is in cu, and ρ is in grams/cm3:
• ρ
• =
• 0.001
• ·
• ∑
• F
• N
• A
• ⁢
• ∑
• i
• =
• 1
• n
• ⁢
• f
• i
• ⁢
• σ
• i
• A
• i
• .